Before 1989, the majority of the chess sets were made of Ivory.

A little bit about Ivory…
The Mammoth Ivory is excavated from the permafrost of the Siberian tundra, which the woolly mammoth inhabited for more than 160,000 years. During the last ice age, the mammoth went extinct as the direct result of rapidly plummeting temperatures that literally flash froze the entire population of Mammuthus primigenius. The dry, cold environment of Siberia combined with the massive sheets of ice from the ice age created the ideal environment for the preservation of Mammoth Ivory. The woolly Mammoth have been entombed under the Siberian permafrost ever since, waiting to be unearthed. For more than 2,000 years, Mammoth Ivory has been traded and it remains a highly prized commodity across the world. While that demand for the Mammoth Ivory has always been higher than its supply, it skyrocketed in 1963 when the CITES agreement was enacted. This agreement banned all sales of new Elephant or Walrus Ivory, in an effort to protect the animals from extinction. As a result, Mammoth Ivory became the only type of animal-based ivory that is exempt from the international trade restrictions because it is considered to be a fossil. The Ivory Chess sets costs around $10,000.
Now Unlike Ivory, Woods for chess boards are much more diverse than those for pieces. There are so many types of wood used for chess boards and sets that we won’t be able to list every single one here.
Now you must be wondering does the variety of wood used to make Chess pieces really matter.
Yes, it does. It depends on the finish, durability and flexibility feature of the particular wood.
Types of Wood:

Sheesham :
Rosewood is mainly called Sheesham in India and golden brown to a darker reddish brown. This is generally grown in the tropical deciduous forest yet softwood. It has a closed-grain texture and is very hard to cut and so makes furniture hard and long-lasting. Rosewood is also used in making musical instruments like pianos, guitars. It is also used in paper industries for making papers sheets. 
Due to high water percentage, it has a higher flexibility; it’s also very cost-effective which makes it a favourite of chess set makers. Sheesham and Rosewood are very popular among the craftsmen because there are fewer chances of cracking and breakage than ebony and sandalwood. Sheesham wood is strong and beautiful for woodworking.
Mostly it’s distinguished for its wood grains and its double colour tone of light and dark yellow/brown. Another reason why it is popular among craftsmen is that it’s cheap and easily available. Did you know: It is capable of withstanding average annual rainfall of up to 2,100 millimetres and droughts of 2-4 months.
Some of our Sheesham Wood Products:
Combo Chess Set | Reproduced Hermann Ohme | Modern Minimalist Style Golden Rosewood Pieces with Walnut Board

Chinese Checkers Game Set with 12-inch Diameter Round Wooden Board

Ebony Wood:

Ebony is a jet black, sometimes with grey or dark brown streaks, the very best quality ebony looks like black plastic. Unlike most woods, ebony is dense enough to sink in water. It is finely textured and has a mirror finish when polished, making it valuable as an ornamental wood. Common uses involve Inlay, carving, musical instrument parts (piano keys, bridges, nuts, etc.), and turned objects.
Ebony is a luxurious wood, often called as the black wood. The natural state is dark brown but a chemical process can make it jet black.
Do you know: Ebony is used by Gibson Guitars for the fingerboards of some fine and classy guitars. Chess makers revere this wood for making luxurious chess sets and chess enthusiasts adore for its elegance and authenticity.
Some of our Ebony Wood Products:
The Imperial Weighted Chess Pieces in Ebony and Boxwood - 3.8" King

Handmade Ebony and Maple Wood Classic Tournament Flat Chessboard

Anjanwood:
East Indian Rosewood has been used for acoustic guitars since the mid-1960s as a substitute for the now-endangered Brazilian Rosewood.
Rosewood like ebony is also considered as a luxury wood. Different variants of this wood comes from different parts it harvested from. It has a reddish tinge, this wood is dense yet not too hard, which makes it perfect for beautiful fingerboards on the guitars.
It is also used in the production of medium to high-end chess pieces, boards & folding sets.
Do you know: Rosewood was used by Fender guitars for their fingerboards from about 1959 onwards and rosewood was always considered a cheaper alternative to Ebony.
Some of our Anjanwood Products
Handmade Classic traditional Tournament Style Anjan wood Tournament Chessboard

 
The Ruffian American Series Staunton Triple Weighted Chess Pieces In Rose / Box Wood - 4.8" King

Budrosewood aka Padauk Wood:
This gorgeous and naturally colorful wood will blow your mind. Padauk elicits all the joys of woodworking between its color, and ease of routing, cutting, sanding and finishing. You'll want to use this one in your most decorative projects like keepsake boxes, musical instruments, fine furniture pieces. African padauk also makes an excellent wood for inlay if you just want to use a little bit. Contrasts well with pale woods like maple and ash, but also darker woods like wenge, walnut, and ebony.
Some of our Padaukwood Products:
Wooden Checkers / Draught Set in Stained Boxwood - 30mm

The Ruffian American Series Staunton Triple Weighted Chess Pieces in African Padauk / Boxwood - 4.8" King

Walnut wood:
Walnut is strong, hard and durable, without being excessively heavy. It has excellent woodworking qualities, and takes finishes well. The wood is light to dark chocolate brown in color and is straight-grained. Wavy grain is present toward the roots, and walnut stumps are often dug out and widely used as a source of highly figured veneer chess boards.
Handmade Double-sided Chess Board made in Walnut: Maple Wood

Boxwood:
In color Boxwood tends to be a light cream to yellow, which tends to darken slightly with prolonged exposure to light. It is a light coloured wood that is used to make chess pieces and squares on chess boards. It is seldom used to make whole chessboards however Boxwood tends to be somewhat difficult to work in flat dimensions, though it is superbly suited for turning.
Commonly used for carving and turning, and the tree’s minute size halts it to smaller projects. Most common uses are chess pieces, musical instruments (flutes, woodwinds, etc.), rulers, , turned objects, and other specially made small items. It is a dense wood that is robust and ages nicely.
Honest chess set traders refer to this as ebonized boxwood, less honest ones will sell them as ebony pieces.
Some of our Boxwood Products:
The Reproduced 2021 Sinquefield Cup Official Chess Pieces

Modern Minimalist Design Golden Rosewood and Boxwood Chess Pieces

Ebonized Boxwood:
In simple words, Ebonised Boxwood is a stained version of Boxwood. It is commonly used to make chess pieces, the black side obviously; a very convincing attempt at producing an Ebony effect.
It’s cheaper than Ebony and is perfect for black chess pieces.
Regular boxwood is light in color and usually used for the white pieces. It’s ebonized for use as black pieces.
Some of our Ebonized Boxwood Products:
Reproduced Eboized Hermann Ohme Minimalist Style Weighted Chess Pieces

Handmade Wooden Staunton Style Tournament Series, German Knight Weighted 3.75" King Chess Pieces Only